Analysis of a Rigid-Body Pose Estimator for Relative Spacecraft Navigation

This study presents a rigorous error analysis of a previously published estimator that determines the single-frame relative pose of two rigid bodies from batches of point and unit vector measurements. The estimator solves a constrained least-squares optimization problem where the pose is represented by a dual quaternion and the properties of pose dual quaternions are exactly satisfied. We develop an eigenvalue-based error analysis and derive analytical expressions for the three-dimensional attitude and translation errors, along with their means and covariance matrices. The closed-form formulas provide significant insights into the distinctive impacts of the point and vector observations’ geometry and noise. They provide valuable tools for performance analysis and prediction. We consider noises both in the body frame and in the reference frame observations. Extensive Monte-Carlo simulations validate the accuracy and consistency of these formulas. Furthermore, we investigate the algorithm’s sensitivity to variations in the number of observations and in the observations’ weight coefficients of the cost function.